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Quantum Hall Effect on Top and Bottom Surface States of Topological Insulator (Bi1&Minus;Xsbx)2Te3 Films

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Quantum Hall Effect on Top and Bottom Surface States of Topological Insulator (Bi1&Minus;Xsbx)2Te3 Films ARTICLE Received 18 Aug 2014 | Accepted 12 Feb 2015 | Published 14 Apr 2015 DOI: 10.1038/ncomms7627 Quantum Hall effect on top and bottom surface states of topological insulator (Bi1 À xSbx)2Te 3 films R. Yoshimi1, A. Tsukazaki2,3, Y. Kozuka1, J. Falson1, K.S. Takahashi4, J.G. Checkelsky1,w, N. Nagaosa1,4, M. Kawasaki1,4 & Y. Tokura1,4 The three-dimensional topological insulator is a novel state of matter characterized by two- dimensional metallic Dirac states on its surface. To verify the topological nature of the surface states, Bi-based chalcogenides such as Bi2Se3,Bi2Te 3,Sb2Te 3 and their combined/mixed compounds have been intensively studied. Here, we report the realization of the quantum Hall effect on the surface Dirac states in (Bi1 À xSbx)2Te 3 films. With electrostatic gate-tuning of the Fermi level in the bulk band gap under magnetic fields, the quantum Hall states with filling factor ±1 are resolved. Furthermore, the appearance of a quantum Hall plateau at filling factor zero reflects a pseudo-spin Hall insulator state when the Fermi level is tuned in between the energy levels of the non-degenerate top and bottom surface Dirac points. The observation of the quantum Hall effect in three-dimensional topological insulator films may pave a way toward topological insulator-based electronics. 1 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan. 2 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. 3 PRESTO, Japan Science and Technology Agency (JST), Chiyoda-ku, Tokyo 102-0075, Japan. 4 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. w Present address: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. Correspondence and requests for materials should be addressed to R.Y. (email: [email protected]). NATURE COMMUNICATIONS | 6:6627 | DOI: 10.1038/ncomms7627 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7627 uantum transport in Dirac electron systems has been surface magnetism and/or Fermi level (EF) that is applicable to attracting much attention for the half-integer quantum quantum computation functions7–9. Although intensive research QHall effect (QHE), as typically observed in graphene1,2. has been carried out for bulk crystals, thin films and field-effect A single Dirac fermion under a magnetic field is known to devices10–17, parasitic bulk conduction and/or disorder in the show the quantized Hall effect with the Hall conductance devices continues to hamper efforts to resolve quantum transport 2 sxy ¼ (n þ 1/2)e /h with n being an integer, e the elemental characteristics of the Dirac states on chalcogenide 3D TIs charge and h the Planck constant. This 1/2 is the characteristic of surfaces. The most venerable example of the QHE with least the Dirac fermion compared with the usual massive electrons. In bulk conduction has been achieved in a 70 nm strained HgTe graphene with such a Dirac electron, however, there is fourfold film18. Compared with the HgTe system, 3D-TIs of Bi- degeneracy due to the spin and valley degrees of freedom, and chalcogenides such as Bi2Se2Te and (Bi1 À xSbx)2Te3 have a good hence the quantized Hall conductance shows up experimentally potential for exploring the Dirac surface states with wide 2 as sxy ¼ 4(n þ 1/2)e /h. The recently discovered topological controllability of transport parameters (resistivity, carrier type insulator (TI) possesses metallic Dirac states on the edge or and density) and band parameters (energy gap, position of Dirac surface of an insulating bulk3–6. With the application of a point and Fermi velocity) by changing the compositions19,20. magnetic field (B), the unique features of Dirac bands may be In the following, we report on the QHE in field-effect exemplified via the formation of Landau levels (LLs). The QHE is transistors based on 3D TI thin films of (Bi1 À xSbx)2Te3 the hallmark of dissipationless topological quantum transport (x ¼ 0.84 and 0.88). With electrostatic gate-tuning of the Fermi originating from one-dimensional chiral edge modes driven by level in the bulk band gap under magnetic fields, quantized Hall 2 cyclotron motion of two-dimensional (2D) electrons. Unlike the plateaus (sxy ¼ ±e /h) at the filling factor n ¼ ±1 are resolved, case of graphene, the degeneracy is completely lifted in the spin- pointing to the formation of chiral edge modes at the top/bottom polarized Dirac state of 2D and three-dimensional (3D) TIs. The surface Dirac states. In addition, the emergence of a sxy ¼ 0 state Hall conductance sxy of 3D TI is expected to be given by the sum around the charge neutral point (CNP) reflects a pseudo-spin of the two contributions from the top and bottom surfaces and Hall insulator state when the location of Fermi level is between 2 hence sxy ¼ (n þ n’ þ 1)e /h with both n and n’ being integers. the non-degenerate top and bottom surface Dirac points. When the two contributions are equivalent, that is, n ¼ n’, only the odd integer QHE is expected. For such 3D TI films, the top and bottom surfaces support surface states with opposite spin- Results momentum locked modes when the top and bottom surfaces are Transport properties with electrostatic gate-tuning. We grew regarded as two independent systems. Such a helicity degree of 3D TI thin films of (Bi1 À xSbx)2Te3 (x ¼ 0.84 and 0.88; both 8 nm freedom in real space can be viewed as the pseudo-spin variable thick) using molecular beam epitaxy (MBE)19 and insulating InP and is hence expected to yield a new quantum state via tuning of (111) substrates. The EF of as-grown film was tuned near to the ad Ti/Au gate 30 AlO 23 nm x x = 0.84 Ti/Au (Bi1–xSbx)2Te3 8 nm B = 3 T InP substrate T = 40 mK b 20 ) Rxx Ω (k yx 10 R xx, Ryx R c 7 0 x = 0.84 6 B = 0 T –10 5 e 4 ) h / 4 2 2 ) e –1 ( Ω xx 3 σ 0 (mT 2 T = 40 mK H 100 mK R 1/ –2 1 200 mK 400 mK 700 mK 0 –4 –6 –4 –2 0 2 4 –4 –2 0 2 4 VG (V) VG – VCNP (V) Figure 1 | Gating of topological insulator (Bi0.16Sb0.84)2Te 3 thin film. (a,b) Cross-sectional schematic and top-view photograph of a Hall-bar device. Broken line in b indicates the position for a. Scale bar, 300 mm. (c) Top gate voltage VG dependence of longitudinal conductivity sxx at various temperatures. (d,e) Effective gate voltage (VG À VCNP) dependence of longitudinal and transverse resistance (Rxx and Ryx) and inverse of Hall coefficient 1/RH under magnetic field B ¼ 3 T at temperature T ¼ 40 mK. The VG for the charge neutral point (CNP), VCNP, is defined as the gate voltage where Ryx is crossing zero. 2 NATURE COMMUNICATIONS | 6:6627 | DOI: 10.1038/ncomms7627 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7627 ARTICLE 50 2 x = 0.84 ν 40 B = 14 T = +1 ) 700 mK 1 Ω 400 mK T = 40 mK 30 ) 200 mK 100 mK h (k 100 mK / 0 200 mK 2 xx 20 T = 40 mK 400 mK e R 700 mK ν ( = –1 n = +2 ν 10 xy –1 = –3 σ n = +1 0 1.0 –2 ν = –1 20 x = 0.84 R B = 14 T n = 0 ) 10 0.5 yx –3 ν = +1 Ω ( 2.0 700 mK T = 40 mK ) h 400 mK n = –1 h (k 100 mK 0 0.0 / / 1.5 200 mK e 200 mK 2 100 mK yx 2 400 mK e T = 40 mK R –10 ) 1.0 700 mK –0.5 ( –20 xx 0.5 Valence band –1.0 σ –30 0.0 –4 –2 0 2 4 –4 –2 0 2 4 VG – VCNP (V) VG – VCNP (V) 120 2 x = 0.88 100 ν B = 14 T = +1 ) 1 80 700 mK Ω 700 mK 400 mK ) 400 mK ν = 0 200 mK h (k 60 100 mK / 0 200 mK 2 xx T = 40 mK 100 mK e ν R 40 T = 40 mK = –2 ( n = +1 20 xy –1 σ ν = –1 0 1.0 –2 20 x = 0.88 ν = 0 R B = 14 T n = 0 ) 10 0.5 yx –3 ν Ω = +1 ( 2.0 700 mK T = 40 mK ) h 400 mK 100 mK h (k 0 0.0 / / 1.5 200 mK 200 mK e 2 yx 400 mK 100 mK n = –1 2 e T = 40 mK ) R –10 700 mK 1.0 –0.5 ( –20 xx 0.5 Top Bottom –1.0 σ –30 0.0 –4 –2 0 2 4 –4 –2 0 2 4 VG – VCNP (V) VG – VCNP (V) Figure 2 | Observation of the quantum Hall effect. (a,b,e,f), Effective gate voltage VG À VCNP dependence of Rxx and Ryx at various temperatures of T ¼ 40–700 mK with application of magnetic field B ¼ 14 T for the x ¼ 0.84 (a,b) and x ¼ 0.88 (e,f) films of (Bi1 À xSbx)2Te 3.(c–e,h), Effective gate voltage VG À VCNP dependence of sxx and sxy at various temperatures of T ¼ 40–700 mK with the application of magnetic field B ¼ 14 T for the x ¼ 0.84 and x ¼ 0.88 films of (Bi1 À xSbx)2Te 3 as deduced from the corresponding Rxx and Ryx data.
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